The present invention relates to an electronic musical instrument, and more particularly to a digital sampling instrument for sampling digital audio data representative of musical sounds.
To electronically simulate the complex musical arrangements produced by bands or orchestras, many different musical notes must be played simultaneously. Typically, these tones are either synthesized according to a mathematical formula, or recreated from digital recordings of musical instruments stored in memory. When the latter is done, each of the notes must be shifted in pitch from waveforms stored in memory.
If this pitch shifting is done by a system whose output is digitally sampled at a fixed sample rate, the process of pitch shifting is an interpolation process. The process of pitch shifting can be viewed as stepping through the waveform in memory with a variable step size which may have a fractional part. The fractional part of any step requires an appropriate interpolation of the surrounding digital samples to produce the correct output waveform point. The number of surrounding points taken into account by the interpolation process is known as the order of the interpolator. The present invention relates to moderate order multichannel interpolators used for the production of audio sounds and music.
Two approaches have been previously used for the interpolation process. The simpler is interpolation by line segment approximation, or "linear" interpolation. The other approach used for interpolation is termed "sinc function" or band-limited interpolation. In this approach, the points to be interpolated are convolved with a windowed sinc (sin(x)/x) function. Because the sinc function is the Fourier transform of a rectangular (or brickwall) function, the output of this interpolator approximates the curve of minimum high frequency energy through the interpolated points.
Both of these interpolation methods produce undesirable artifacts when used for pitch shifting. While the artifacts are minimized by adequately high order (15 points or more) bandlimited interpolation, it would be advantageous to provide an adequate interpolator of moderate order usable for pitch shifting of musical sounds.